Optics for an extended depth of field

ABSTRACT

An optical imaging assembly ( 22 ) having cylindrical symmetry, comprising a plurality of lenses having surfaces with curvatures and spacings between the surfaces, such that an optical image formed by the plurality of lenses has a defocus aberration coefficient greater than 0.1 at a focal plane of the assembly.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional PatentApplication 60/735,441, filed Nov. 10, 2005. This application is acontinuation-in-part of U.S. patent application Ser. No. 10/541,967,which was filed Jul. 8, 2005, in the national phase of PCT PatentApplication PCT/IL2004/000040, claiming the benefit of U.S. ProvisionalPatent Application 60/440,561, filed Jan. 16, 2003, and is also acontinuation-in-part of U.S. patent application Ser. No. 11/278,255,filed 31 Mar., 2006. All of these related applications are incorporatedherein by reference.

FIELD OF THE INVENTION

The present invention relates generally to digital imaging, andspecifically to optics and methods for designing digital cameras with anenhanced depth of field.

BACKGROUND OF THE INVENTION

The objective optics used in digital cameras are typically designed soas to minimize the optical point spread function (PSF) and maximize themodulation transfer function (MTF), subject to the limitations of size,cost, aperture size, and other factors imposed by the cameramanufacturer. The PSF of the resulting optical system may still varyfrom the ideal due to focal variations and aberrations. A number ofmethods are known in the art for measuring and compensating for such PSFdeviations by digital image processing. For example, U.S. Pat. No.6,154,574, whose disclosure is incorporated herein by reference,describes a method for digitally focusing an out-of-focus image in animage processing system. A mean step response is obtained by dividing adefocused image into sub-images, and calculating step responses withrespect to the edge direction in each sub-image. The mean step responseis used in calculating PSF coefficients, which are applied in turn todetermine an image restoration transfer function. An in-focus image isobtained by multiplying this function by the out-of-focus image in thefrequency domain.

As another example, U.S. Pat. No. 6,567,570, whose disclosure isincorporated herein by reference, describes an image scanner, which usestargets within the scanner to make internal measurements of the PSF.These measurements are used in computing convolution kernels, which areapplied to images captured by the scanner in order to partiallycompensate for imperfections of the scanner lens system.

It is also possible to add a special-purpose blur to an image so as tocreate invariance to certain optical aberrations. Signal processing isthen used to remove the blur. A technique of this sort is described byKubala et al., in “Reducing Complexity in Computational ImagingSystems,” Optics Express 11 (2003), pages 2102-2108, which isincorporated herein by reference. The authors refer to this technique as“Wavefront Coding.” A special aspheric optical element is used to createthe blur in the image. This optical element may be a separatestand-alone element, or it may be integrated into one or more of thelenses in the optical system. Optical designs and methods of imageprocessing based on Wavefront Coding of this sort are described, forexample, in U.S. Pat. No. 5,748,371 and in U.S. Patent ApplicationPublications US 2002/0118457 A1, US 2003/0057353 A1 and US 2003/0169944A1, whose disclosures are incorporated herein by reference.

SUMMARY OF THE INVENTION

In embodiments of the present invention, an optical imaging assemblythat may be used in a digital camera is constructed so as to generate adistorted image at an imaging plane of the assembly. The digital cameraincorporates a sensor at the imaging plane, and the distorted imageformed on the sensor is corrected by a deconvolution engine so as toproduce an undistorted image. The optical imaging assembly is configuredto produce a high defocus aberration coefficient, greater thanapproximately 0.1, across the distorted image when the image isoptimally focused to a focal plane of the assembly.

The high defocus aberration coefficient causes a modulation transferfunction (MTF) for the assembly to have generally equal low values forall objects in a large field, typically from infinity to approximately10 cm from the assembly. Because of the equal values of the MTF at thedifferent object distances within the field, the deconvolution enginemay be configured to improve the MTF of all the images at the differentobject distances. The final images thus produced by the assembly and thedeconvolution engine are substantially free of aberrations for allobjects within the field, so that the digital camera has a depth offield which is significantly higher than depths of field of prior artcameras.

In some embodiments the imaging assembly is designed by assuming that avirtual phase plate is added to the assembly, the virtual phase platehaving characteristics that generate aberration coefficients which arethe negatives of those required by the deconvolution engine. Theassembly with the phase plate is configured to give an undistortedimage.

There is therefore provided, according to an embodiment of the presentinvention, an optical imaging assembly having cylindrical symmetry,including a plurality of lenses having surfaces with curvatures andspacings between the surfaces, such that an optical image formed by theplurality of lenses has a defocus aberration coefficient greater than0.1 at a focal plane of the assembly. The defocus aberration coefficientmay be greater than or equal to 0.6, and less than or equal to 0.9. Afifth order spherical aberration is typically between −0.2 and −0.3, aseventh order spherical aberration may be −0.5, and a ninth orderspherical aberration may be 0.

In some embodiments, the curvatures are non-logarithmic.

Typically, the optical image is of one or more objects within a field ofview subtending up to 33° to an optic axis of the assembly.

In an embodiment the optical image is of one or more objects which arelocated at distances greater than or equal to 10 cm from the assembly.Typically, the assembly is configured so that a modulation transferfunction generated by the one or more objects at the focal plane is lessthan or equal to 0.35 for spatial frequencies greater than 50 cycles permm.

In a disclosed embodiment the optical image has an extent of a pointspread function equal to or greater than 14 μm at the focal plane.

There is further provided, according to an embodiment of the presentinvention, a method for optical imaging, including:

formulating an optical specification of an optical imaging assemblyincluding optical elements having surfaces, the optical specificationincluding one or more aberration coefficients;

generating a virtual phase element having phase coefficients which arenegatives of the aberration coefficients;

generating a design of the optical assembly including the opticalelements and the virtual phase element so as to determine curvatures andspacings of the surfaces that will focus an image of an object on afocal plane of the assembly in the presence of the virtual phaseelement; and

fabricating the optical assembly in accordance with the curvatures andspacings determined by the design.

In a disclosed embodiment, the method includes generating a digitalfilter to compensate for the one or more aberration coefficients, andcoupling the digital filter to the optical assembly so that a filteredimage formed by the digital filter from the image on the focal plane isfree of aberrations. Typically, the filtered image is free ofaberrations for the object being located at a distance greater than 10cm from the optical assembly.

There is further provided, according to an embodiment of the presentinvention, an optical imaging assembly having cylindrical symmetry,including a plurality of lenses having surfaces with curvatures andspacings between the surfaces, such that an optical image formed by theplurality of lenses at a focal plane of the assembly has a modulationtransfer function (MTF) for spatial frequencies greater than 50 cyclesper millimeter that is less than or equal to 0.35.

There is further provided, according to an embodiment of the presentinvention, a method for forming an optical imaging assembly, including,providing a plurality of lenses having cylindrical symmetry and surfaceswith curvatures and spacings between the surfaces; and

arranging the lenses so that an optical image formed by the plurality oflenses has a defocus aberration coefficient greater than 0.1 at a focalplane of the assembly.

There is further provided, according to an embodiment of the presentinvention, apparatus for optical imaging, including:

an optical imaging assembly including optical elements having surfaces;and

a processor which is configured to:

formulate an optical specification of the optical imaging assembly, theoptical specification including one or more aberration coefficients,

generate a virtual phase element having phase coefficients which arenegatives of the aberration coefficients;

generate a design of the optical assembly including the optical elementsand the virtual phase element so as to determine curvatures and spacingsof the surfaces that will focus an image of an object on a focal planeof the assembly in the presence of the virtual phase element; and

-   -   fabricate the optical assembly in accordance with the curvatures        and spacings determined by the design.

There is further provided, according to an embodiment of the presentinvention, a method for forming an optical imaging assembly, including:

providing a plurality of lenses having cylindrical symmetry and surfaceswith curvatures and spacings between the surfaces; and

arranging the lenses so that an optical image formed by the plurality oflenses at a focal plane of the assembly has a modulation transferfunction (MTF) for spatial frequencies greater than 50 cycles permillimeter that is less than or equal to 0.35.

There is further provided, according to an embodiment of the presentinvention, an optical imaging assembly, including:

an aperture having a semi-diameter of 7.5·10⁻¹ mm; and

a plurality of lenses having surfaces with curvatures and spacingsbetween the surfaces, wherein respective surfaces of the plurality oflenses are defined by an equation

$z = {\frac{c\; r^{2}}{1 + \sqrt{1 - {\left( {1 + k} \right)c^{2}r^{2}}}} + {\sum\limits_{n = 2}^{n = 8}{\alpha_{n}r^{2\; n}}}}$

where z is a sag of the surface,

-   -   r is a radius measured to an optic axis of the assembly,    -   c, k are respective curvature and conic constants for the        surface, and    -   α₂, . . . α₈ are parameters for the surface,

the lenses including:

a first aspheric lens following the aperture, having a refractive index1.53, a first surface wherein c=9.57·10⁻², k=9.74·10¹, α₂=−1.38·10⁻²,α₃=−9.0·10⁻¹, α₄=2.83, α₅=−2.26, α₆=−2.96, α₇=2.69, α₈=1.61, and asecond surface wherein c=−4.46·10⁻¹, k=0, α₂=−9.83·10⁻², α₃=1.24·10⁻¹,α₄=−4.25·10⁻¹, α₅=7.62·10⁻¹, α₆=−8.04·10⁻¹, α₇=4.73·10⁻¹, α₈=−1.28·10⁻¹;

a second aspheric lens following the first aspheric lens, having arefractive index 1.61, a third surface wherein c=−7.60·10⁻¹, k=−3.37,and absolute values of α₂, α₃, α₄, α₅, α₆, α₇, α₈ less than 1, and afourth surface wherein c=−2.42·10⁻¹, k=2.38, and absolute values of α₂,α₃, α₄, α₅, α₆, α₇, α₈ less than 1; and

a third aspheric lens following the second aspheric lens, having arefractive index 1.53, a fifth surface wherein c=8.1·10⁻¹, k=−4.03, andabsolute values of α₂, α₃, α₄, α₅, α₆, α₇, α₈ less than 1, and a sixthsurface wherein c=5.17·10⁻¹, k=4.07, and absolute values of α₂, α₃, α₄,α₅, α₆, α₇, α₈ less than 1.

The present invention will be more fully understood from the followingdetailed description of the embodiments thereof, taken together with thedrawings in which:

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram that schematically illustrates a digitalcamera, in accordance with an embodiment of the present invention;

FIG. 2 is a schematic, pictorial illustration of a system for designinga digital camera, in accordance with an embodiment of the presentinvention;

FIG. 3A is a schematic, pictorial illustration showing conceptualelements of a digital camera used in a design process, in accordancewith an embodiment of the present invention;

FIG. 3B is a plot of modulation transfer functions (MTF) for a digitalcamera with and without application of a deconvolution filter, inaccordance with an embodiment of the present invention;

FIG. 4 is a flow chart that schematically illustrates a method fordesigning a digital camera, in accordance with an embodiment of thepresent invention;

FIGS. 5A-5C are schematic, perspective plots of DCF kernels used in adigital camera, in accordance with an embodiment of the presentinvention;

FIG. 6 is an image that simulates the output of an image sensor usingobjective optics with specifications that have been relaxed inaccordance with an embodiment of the present invention;

FIG. 7 is an image that simulates the effect of application of anappropriate DCF to the image of FIG. 6, in accordance with an embodimentof the present invention;

FIG. 8 is a schematic pictorial representation of a camera imaging alarge depth of field, in accordance with an embodiment of the presentinvention;

FIG. 9 schematically shows detail of a camera sensor, in accordance withan embodiment of the present invention;

FIG. 10 is a flowchart schematically describing procedures performed indesigning a digital camera, in accordance with an embodiment of thepresent invention;

FIGS. 11A-11E schematically show results generated in the procedures ofFIG. 10, in accordance with an embodiment of the present invention;

FIGS. 12A-12G show Modulation Transfer Function curves for an exemplaryoptical imaging assembly, in accordance with an embodiment of thepresent invention; and

FIG. 13 is a schematic diagram of the exemplary optical imagingassembly, in accordance with an embodiment of the present invention.

DETAILED DESCRIPTION OF EMBODIMENTS Definitions

The following is a non-exhaustive list of technical terms that are usedin the present patent application and in the claims. Although theseterms are used herein in accordance with the plain meaning accorded theterms in the art, they are listed below for the convenience of thereader in understanding the following description and the claims.

-   -   Pitch of a detector array refers to the center-to-center        distance between elements of the array.    -   Cylindrical symmetry describes a structure, such as a simple or        compound lens, which has an optical axis such that the structure        is invariant under rotation about the optical axis for any and        all angles of rotation.    -   Point spread function (PSF) is the impulse response of an        optical system in the spatial domain, i.e., the image formed by        the system of a bright point object against a dark background.    -   Extent of the PSF is the full width at half maximum (FWHM) of        the PSF.    -   Optical transfer function (OTF) is the two-dimensional Fourier        transform of the PSF to the frequency domain. Because of the        ease with which a PSF may be transformed into an OTF, and vice        versa, computation of the OTF is considered to be equivalent to        computation of the PSF for the purposes of the present        invention.    -   Modulation transfer function (MTF) is the modulus of the OTF.    -   Optical radiation refers to electromagnetic radiation in any of        the visible, infrared and ultraviolet regions of the spectrum.

System Overview

FIG. 1 is a block diagram that schematically illustrates a digitalcamera 20, in accordance with an embodiment of the present invention.The camera comprises refractive objective optics 22, which focus animage onto an image sensor 24, so that a surface of the sensor acts as afocal plane of the optics. Optics 22 are also referred to herein asoptical imaging assembly 22. Optics 22 are designed in an iterativeprocess together with a deconvolution engine 26 that operates on imagedata that are output by image sensor 24. The deconvolution engineapplies one or more digital filters, typically comprising at least onedeconvolution filter (DCF), to the image data. The design process andmethod of filtering are described in detail hereinbelow. The DCF kernelis typically chosen so as to correct for blur in the image formed byoptics 22. After filtering, the image data are processed by an imagesignal processor (ISP) 28, which performs standard functions such ascolor balance and format conversion and outputs the resulting image.

The optical and digital processing schemes illustrated in FIG. 1 areshown here solely for the sake of example, as an aid to understandingthe techniques and tools that are described hereinbelow. In practice,the principles of the present invention may be applied in conjunctionwith a wide variety of electronic imaging systems, using substantiallyany sort of optical design and substantially any type of image sensor,including both two-dimensional detector matrices and linear detectorarrays, as are known in the art. Deconvolution engine 26 and ISP 28 maybe implemented as separate devices or as a single integrated circuitcomponent. In either case, the deconvolution engine and ISP aretypically combined with other I/O and processing elements, as are knownin the art. In the context of the present patent application, the term“digital camera” should therefore be understood as referring to any andall sorts of electronic imaging systems that comprise an image sensor,objective optics for focusing optical radiation onto the image sensor,and electronic circuits for processing the sensor output.

FIG. 2 is a schematic, pictorial illustration showing a system 30 fordesigning a digital camera, in accordance with an embodiment of thepresent invention. System comprises a digital processing design station32 and an optical design station 34. Processing design station 32receives a camera specification as input, from a camera manufacturer,for example, specifying the key dimensions, sensor type and desiredoptical characteristics (referred to hereinafter as the target opticalspecification) of the camera. The specified optical characteristics mayinclude, for example, the number of optical elements, materials,tolerances, focal length, magnification, aperture (F-number), depth offield, and resolution performance. The optical resolution performance istypically defined in terms of the MTF, but it may alternatively bespecified in terms of PSF, wavefront quality, aberrations, and/or othermeasures of optical and image quality that are known in the art.

Processing design station 32 analyzes and modifies the target opticalspecification, taking into account the expected operation of engine 26,in order to provide a modified optical specification to the opticaldesign station. Typically, both the original camera specification andthe modified optical specification use cylindrically-symmetrical opticalelements. Specialized phase plates or other elements that break thecylindrical symmetry of the optics are generally undesirable, due totheir added cost, and engine 26 is able to correct the aberrations ofoptics 22 without requiring the use of such elements. In addition,processing design station 32 may compute and provide to optical designstation 34 a merit function, indicating target values of the aberrationsof optics 22 or scoring coefficients to be used in weighting theaberrations in the course of optimizing the optical design. Theaberrations express deviations of the optical wavefront created byoptics 22 from the ideal, and may be expressed, for example, in terms ofZernike polynomials or any other convenient mathematical representationof the wavefront that is known in the art.

Optical design station 34 is typically operated by a lens designer, inorder to produce a lens design according to the modified opticalspecification provided by processing design station 32. The processingdesign station determines the optimal DCF (and possibly other filters)to be used in engine 26 in conjunction with this lens design. The DCFcomputation is tied to the specific lens design in question so that thefilter coefficients reflect the “true” PSF of the actual optical systemwith which the DCF is to be used.

The processing design station then evaluates the optical design togetherwith the DCF in order to assess the combined result of the expectedoptical quality of optics 22 and the enhancement expected from engine26, and to compare the result to the target optical specification. Theassessment may take the form of mathematical analysis, resulting in aquality score. A quality scoring schemes that may be used in thiscontext is described hereinbelow. Alternatively, other quality scoringschemes may be used, such as that described, for example, in theabove-mentioned PCT publication WO 2004/063989 A2. Alternatively oradditionally, station 32 may generate and display a simulated image 36,which visually demonstrates the output image to be expected from thecamera under design based on the current choice of opticalspecifications and DCF.

If the result of the analysis by station 32 indicates that the combinedoptical and DCF design will meet the target specifications, then thecomplete camera design, including optics and DCF, is output forproduction. Otherwise, the processing design station may perform furtherdesign iterations internally, or it may generate a further modifiedoptical specification, which it passes to optical design station 34 forgeneration of a modified optical design. This process may continueiteratively until a suitable optical design and DCF are found. Detailsof this process are described hereinbelow with reference to FIG. 4.

Typically, stations 32 and 34 comprise general-purpose computers runningsuitable software to carry out the functions described herein. Thesoftware may be downloaded to the computers in electronic form, over anetwork, for example, or it may alternatively be furnished on tangiblemedia, such as optical, magnetic, or electronic memory media.Alternatively, some of the fractions of stations 32 and/or 34 may beimplemented using dedicated or programmable hardware components. Thefunctions of optical design station 34 may be carried out usingoff-shelf optical design software, such as ZEMAX® (produced by ZEMAXDevelopment Corp., San Diego, Calif.). Although stations 32 and 34 areshown and described, for the sake of conceptual clarity, as separatecomputer workstations, the functions of these stations may alternativelybe combined in a single physical machine, running software processes forboth optical design and digital processing design.

FIG. 3A is a schematic, pictorial illustration showing conceptualelements of camera 20, as they are applied in the design process used insystem 30, in accordance with an embodiment of the present invention.System 30 takes engine 26 into account in the design of optics 22, asexplained hereinabove, and thus relates to the DCF as a sort of “virtuallens” 40. In other words, the design constraints on the actual objectiveoptics are relaxed by the use of this virtual lens, as though theoptical designer had an additional optical element to incorporate in thedesign for purposes of aberration correction. The virtual lens that isimplemented in engine 26 is chosen, in conjunction with the actualoptical lenses, to give an image output that meets the manufacturer'scamera specifications.

FIG. 3B is a plot showing the MTF of a camera designed using system 30,in accordance with an embodiment of the present invention. The plotincludes an uncorrected curve 44, corresponding to the modified opticalspecification generated by station 32 for use in designing optics 22 onstation 34. The low MTF permitted by curve 44 is indicative of theexpected improvement in MTF that can be achieved by use of DCF 26. Acorrected curve 46 shows the net MTF of the camera that is achieved byapplying the DCF to the image sensor output. These curves show the MTFat the center of the optical field, with the object at a certaindistance from the camera. In practice, the MTF may be specified atmultiple different focal depths and field angles.

The design concept exemplified by FIGS. 3A and 3B permits the cameramanufacturer to achieve the desired level of optical performance withfewer, smaller and/or simpler optical components than would be requiredto achieve the same result by optical means alone. Additionally oralternatively, the camera may be designed for enhanced performance, suchas reduced aberrations, reduced F-number, wide angle, macro operation,or increased depth of field.

Detailed Design Process

FIG. 4 is a flow chart that schematically illustrates a method fordesigning a digital camera, in accordance with an embodiment of thepresent invention. The method will be described hereinbelow, for thesake of clarity, with reference to camera 20 and system 30, although theprinciples of this method may be applied generally to other cameras andusing other design systems.

The point of departure of the design is the camera specification, asnoted above. Processing design station 32 translates the target opticalspecification of the camera into a modified optical specification, at aspecification translation step 50. For this purpose, station 32 uses anestimate of the DCF to be implemented in the camera. The imageenhancement to be expected due to this DCF is then applied to theoptical specification in order to estimate how far the optical designparameters, such as the MTF, can be relaxed.

Image enhancement by the DCF, however, tends to amplify noise in theoutput of image sensor 24. Generally speaking, the noise gain NG isproportional to the norm of the DCF (√{square root over (D^(t)D)},wherein D is the DCF kernel and the superscript t indicates theHermitian transpose). Therefore, in estimating the DCF, and hence inestimating the degree to which the optical design parameters can berelaxed the processing design station uses the maximum permissible noisegain as a limiting condition. Typically, engine 26 may also comprise anoise filter. The limit placed on the DCF coefficients by the noise gainmay thus be mitigated by the noise reduction that is expected due to thenoise filter. In other words, the norm of the DCF kernel isapproximately given by the product of the maximum permissible noise gainwith the expected noise reduction factor (i.e., the ratio of image noisefollowing the noise filter to image noise without noise filtering).Alternatively, a more accurate estimate of the overall noise gain may beobtained by taking the norm of the product of the noise filtermultiplied by the DCF in the frequency domain.

In order to determine the noise gain and permissible MTF reduction, theOTF may be assumed, at first approximation, to be linear as a functionof spatial frequency q, which is normalized to the Nyquist frequency ofimage sensor 24:

OTF=1−λq}q≦1/λ

OTF=0}q>1/λ  (1)

The PSF may be determined analytically from the OTF of equation (1).Because of the zeroes in the OTF, the frequency-domain representation ofthe DCF to be used in the camera may be estimated as:

$\begin{matrix}{{DCF} = \frac{OTF}{{OTF}^{2} + \alpha^{2}}} & (2)\end{matrix}$

wherein α is a small number that keeps the DCF from exploding for smallPSF.

The noise gain NG due to the DCF of equation (2) depends on the twoparameters λ, α:

$\begin{matrix}{({NG})^{2} = {\frac{\pi}{\lambda^{2}}\left\lbrack {\frac{{arc}\; {\tan \left( {1/\alpha} \right)}}{\alpha} - {\ln \left( {\frac{1}{\alpha^{2}} + 1} \right)}} \right\rbrack}} & (3)\end{matrix}$

These parameters are chosen so that the noise gain does not exceed atarget bound, for example, 300%. If the original camera specificationsinclude a noise figure, the maximal permissible noise gain may bedetermined by comparing the expected noise characteristic of imagesensor 24 to the noise specification. As noted above, digital smoothingof the noise in the output image may also be taken into account in orderto permit the constraint on noise gain in the DCF to be relaxed.

Various noise removal methods, as are known in the art, may be used inengine 26. For example, a morphological operation may be used toidentify edges in the image, followed by low-pass filtering of non-edgeareas. The choice of noise removal method to be used in engine 26,however, is beyond the scope of the present invention.

Having chosen appropriate values of the parameters, the average MTF overthe normalized frequency range [0,1] is given by:

$\begin{matrix}{{MTF}_{avg} = {\frac{1}{\lambda}\left( {1 - {\alpha \star {{arc}\; {\tan \left( {1/\alpha} \right)}}}} \right)}} & (4)\end{matrix}$

The formulas given above in equations (3) and (4) apply for λ>1, whichwill be the case in most simple camera designs. Alternative estimatesmay be developed for high-resolution cameras in which λ<1. For α<<1, thenoise gain may be expressed as a polynomial series in α or in the form:

$\begin{matrix}{{NG}^{2} = {\frac{\pi}{\lambda^{2}}\left( {\frac{\pi^{2}}{4\left( {1 - {\lambda \star {MTF}_{avg}}} \right)} - {2\; {\ln \left( \frac{\pi}{2\left( {1 - {\lambda \star {MTF}_{avg}}} \right)} \right)}}} \right)}} & (5)\end{matrix}$

Other representations will be apparent to those skilled in the art.

Equations (4) and (5) may be used in estimating how far the MTF ofoptics 22 may be reduced relative to the original target specification,subject to a given noise gain limit. This reduction factor may beapplied, for example, to the MTF required by the original cameraspecification at a benchmark frequency, such as half the Nyquistfrequency. In the example shown in FIG. 3B, the target MTF has beenreduced to about ⅓ of its original specified value. The MTF will berestored in the output image from camera 20 by operation of the DCF inengine 26.

Referring back now to FIG. 4, processing design station 32 may alsogenerate a merit function at step 50 for use by the optical designer.The merit function may take the form of aberration scores, which areassigned to each significant aberration that may characterize optics 22.For this purpose, the aberrations may be expressed, for example, interms of the Zernike polynomials, for each of the colors red, green andblue individually. Standard software packages for optical design, suchas ZEMAX, are capable of computing the Zernike polynomial coefficientsfor substantially any design that they generate. Values of the meritfunctions may be provided in tabular form. Generation of these values isdescribed in detail in the above-mentioned PCT Publication WO2004/063989 A2.

Alternatively or additionally, processing design station 32 may generatetarget wavefront characteristics that the optical design should achievein the image plane (i.e., the plane of sensor 24). These wavefrontcharacteristics may conveniently be expressed in terms of values of theaberrations of optics 22, such as Zernike coefficient values. Typically,aberrations that can be corrected satisfactorily by deconvolution engine26 may have high values in the optical design, whereas aberrations thatare difficult to correct should have low values. In other words, anaberration that would have a high score in the merit function will havea low target value, and vice versa. The target aberration values can beseen as the inverse of the wavefront corrections that can be achieved by“virtual lens” 40. The target aberration values may also includeaberrations that reduce the sensitivity of the optics to variousundesirable parameters, such as manufacturing deviations and defocus.

An optical designer working on station 34 uses the specification, alongwith the merit function and/or aberration target values provided at step50, in generating an initial design of optics 22, at an optical designstep 52. The designer may use the merit function in determining a designscore, which indicates how to trade off one aberration against anotherin order to generate an initial design that maximizes the total of themerit scores subject to the optical specification. Additionally oralternatively, the optical designer may insert a dummy optical element,with fixed phase characteristics given by the target aberration valuesas an additional element in the optical design. This dummy opticalelement expresses the wavefront correction that is expected to beachieved using engine 26 and thus facilitates convergence of thecalculations made by the optical design software on station 34 to thedesired design of the elements of optics 22.

Control of the design process now passes to processing design station32, in a design optimization stage 53. The processing design stationanalyzes the optical design, at a design analysis step 54. The analysisat this step may include the effect of virtual lens 40. At step 54,station 32 typically computes the optical performance of the optics as afunction of wavelength and of location in the image plane. For example,station 32 may perform an accurate ray trace computation based on theinitial optical design in or to calculate a phase model at the imageplane, which may be expressed in terms of Zernike polynomialcoefficients. The total aberration—and hence the PSF—at any point in theimage plane may be obtained from the total wavefront aberration, whichis calculated by summing the values of the Zernike polynomials.

Station 32 determines a design quality score, at a scoring step 55.Typically, this score combines the effects of the PSF on imageresolution and on artifacts in the image, and reflects the ability ofengine 26 to compensate for these effects. The score measures the extentto which the current optical design, taken together with filtering byengine 26, will satisfy the camera specification that was originallyprovided as input to station 32 as input to step 50.

In an exemplary embodiment, the score computed at step 55 is based onthe camera specification and on a set of weights assigned to eachparameter in the camera specification. The camera specification isexpressed in a list of desired parameter values at various image planelocations and wavelengths, such as:

-   -   MTF    -   Geometrical distortion    -   Field of view    -   Chromatic aberrations    -   Chief ray angle    -   F-number    -   Relative illumination    -   Artifact level    -   Glare    -   Back focal length    -   Manufacturing tolerances    -   Depth of field    -   Noise level    -   Total length of optics.        The weight assigned to each parameter is typically determined by        its scaling, subjective importance, and likelihood of satisfying        the desired parameter value relative to other parameters.

The overall score is computed by summing the weighted contributions ofall the relevant parameters. In this embodiment, if a given parameter iswithin the specified range, it makes no contribution to the score. Ifthe value is outside the specified range, the score is decreased by thesquare difference between the parameter value and the closestpermissible value within the specified range, multiplied by theappropriate weight. A design that fully complies with the cameraspecification will thus yield a zero score, while non-compliance willyield negative values. Alternatively, other parameters and other methodsmay be used in computing numerical values representing how well thecurrent design satisfies the camera specification.

The score computed at step 55 is assessed to determine whether itindicates that the current design is acceptable, at a quantitativeassessment step 56. If the design does not meet the specification,station 32 modifies the optical design parameters at an optimizationstep 58. For this purpose, the station may estimate the effects of smallchanges in the aberrations on the PSF. This operation gives amulti-dimensional gradient, which is used in computing a change to bemade in the optical design parameters by linear approximation. The DCFparameters may be adjusted accordingly. A method for computing and usinggradients of this sort is described, for example, in the above-mentionedPCT Publication WO 2004/063989 A2. The results of step 58 are input tostep 54 for recomputation of the optical performance analysis. Theprocess continues iteratively through steps 55 and 56 until the designquality score reaches a satisfactory result.

Once the design has converged, the design parameters are presented byprocessing design station 32 to the system operator, at a designchecking step 60. Typically, the system operator reviews the opticaldesign (as modified by station 32 in step 58, if necessary), along withthe results of the design analysis performed at step 54. Additionally oralternatively, the optical design and DCF may be used at this point ingenerating a simulated output image, representing the expectedperformance of the camera in imaging a known scene or test pattern.(Exemplary simulated images of this sort are shown below in FIGS. 6 and7.) The system operator reviews the design in order to verify that theresults are indeed satisfactory for use in manufacture of camera 20. Ifnot, the operator may change certain parameters, such as specificationparameters and/or scoring weights, and return to stage 53.Alternatively, if it appears that there are serious problems with thedesign, the operator may initiate changes to the original cameraspecification and return the process to step 50. This sort of operatorinvolvement may also be called for if stage 53 fails to converge to anacceptable score at step 56.

Once the design is found to be acceptable, processing design station 32generates tables of values to be used in camera 20, at a DCF creationstep 62. Typically, because of the non-uniform performance of optics 22,the DCF tables vary according to location in the image plane. In anexemplary embodiment, a different DCF kernel is computed for each regionof 50×50 pixels in image sensor 24.

Furthermore, when sensor 24 is a color image sensor, different kernelsare computed for the different color planes of sensor 24. For example,referring back to FIG. 3A, common mosaic image sensors may use a Bayerpattern of red, green, and blue pixels 42. In this case, the output ofthe image sensor is an interleaved stream of sub-images, comprisingpixel samples belonging to different, respective colors. DCF 26 appliesdifferent kernels in alternation, so that the pixels of each color arefiltered using values of other nearby pixels of the same color.Appropriate kernel arrangements for performing this sort of filteringare described in U.S. Provisional Patent Application 60/735,519, filedNov. 10, 2005, which is assigned to the assignee of the present patentapplication and is incorporated herein by reference.

FIGS. 5A, 5B and 5C are schematic, perspective plots of DCF kernels 70,72 and 74 for red, green, and blue pixels, respectively, which arecomputed in accordance with an embodiment of the present invention. Eachkernel extends over 15×15 pixels, but contains non-zero values only atpixels of the appropriate color. In other words, in red kernel 70, forexample, in each square of four pixels, only one—the red pixel—has anon-zero value. Blue kernel 74 is similarly constructed, while greenkernel 72 contains two non-zero values in each four-pixel square,corresponding to the greater density of green pixels in the Bayermatrix. In each kernel, the central pixel has a large positive value,while surrounding values are lower and may include negative values 76.As explained above, the DCF values are chosen so that the norm does notexceed the permitted noise gain.

Referring back to FIG. 4, design station 32 uses the DCF tables fromstep 62 and the optical design output from stage 53 in simulating theperformance of camera 20, at a simulation step 64. The simulation mayalso use characteristics, such as noise figures, of image sensor 24 thatis to be installed in the camera, as well as other factors, such asmanufacturing tolerances to be applied-in-producing the camera and/oroperation of ISP 28. The results of this step may include simulatedimages, like image 36 (FIG. 2), which enable the system operator tovisualize the expected camera performance.

FIGS. 6 and 7 are images that simulate the expected output of camera 20,as may be generated at step 64, in accordance with an embodiment of thepresent invention. FIG. 6 shows a standard test pattern as it would beimaged by optics and captured by image sensor 24, without the use of DCF26. The image of the test pattern is blurred, especially at higherspatial frequencies, due to the low MTF of camera 20. (The MTF is givenroughly by uncorrected curve 44 in FIG. 3B.) In addition, the imagepixels are decimated due to the use of a color mosaic sensor, and randomnoise is added to the image corresponding to the expected noisecharacteristics of the image sensor.

FIG. 7 shows the image of FIG. 6 after simulation of processing by DCF26, including noise removal as described hereinbelow. The MTF of thisimage is given roughly by curve 46 in FIG. 3B. (The aliasing apparent inthe images of the high-frequency test patterns is the result of a truesimulation of the performance of a low-resolution image sensor followingDCF processing.) The system operator, viewing this image, is able toascertain visually whether the camera performance will meet the originalcamera specifications that were provided at step 50.

The system operator's visual assessment is combined with the numericalresults of the design analysis, in order to determine whether theoverall performance of the design is acceptable, at an acceptance step66. If there are still flaws in the simulated image or in other designquality measures, the design iteration through stage is repeated, asdescribed above. Alternatively, in case of serious flaws, the cameraspecification may be modified, and the process may return to step 50.Otherwise, system 30 outputs the final optical design and DCF tables,together with other aspects of the hardware circuit implementation ofthe camera (such as a netlist of engine 26), and the design process isthus complete.

Optionally, after prototypes of optics 22 have been fabricated, the DCFtables may be tested and modified in a testbench calibration procedure.Such a procedure may be desirable in order to correct the DCF fordeviations between the actual performance of the optics and thesimulated performance that was used in the design process of FIG. 4. Acalibration procedure that may be used for this purpose is described inthe above-mentioned provisional application.

Zernike Polynomials

As stated above, optic aberrations may be quantified in terms ofcoefficients of the Zernike polynomials. The Zernike polynomials aredescribed, for example, by Born & Wolf in Principles of Optics, 7^(th)edition (Cambridge University Press, 2002), in section 9.2, pages523-527, and in Appendix VII, pages 905-910, which are incorporatedherein by reference. Table I below lists different Zernike polynomials:

TABLE I Poly- nomial Name Notes Z1 Piston Mean value of the wavefront Z2X-tilt Deviation in the sagittal direction Z3 Y-tilt Deviation in thetangential direction Z4 Defocus Quadratic term due to out of focus Z5X-astigmatism Horizontally oriented cylinder and out of focus Z6Y-astigmatism Vertically oriented cylinder and out of focus Z7 X-comaComatic flaring in the x-direction Z8 Y-coma Comatic flaring in they-direction Z9 Third order spherical Third order spherical aberration,and defocus Z10-Z16 Fifth order aberrations Z17-Z25 Seventh orderaberrations Z26-Z36 Ninth order aberrations Z37 11^(th) order aberration

As shown in Table I, Z4 and Z9 contribute to spherical aberrations. Inaddition, Z16, Z25, Z36, and Z37 also contribute to sphericalaberrations. Z1, Z2, and Z3 do not contribute to loss of resolution ofthe imaging system.

Extended Depth of Field

FIG. 8 is a schematic pictorial representation of camera 20 imaging alarge depth of field, in accordance with an embodiment of the presentinvention. In the following description, unless otherwise stated, it isassumed that the iterative detailed design process described above withreference to FIG. 4, and the design procedures described below withreference to FIG. 10, are followed. Also in the following description,the specifications of Tables II, III, IV, V, and VI are exemplary, andit will be understood that embodiments of the present invention providenumerous camera assemblies having a large depth of field.

A camera specification, corresponding to that provided to design station32 (FIG. 1) at step 50 (FIG. 4), is assumed to include cylindricallysymmetric optics 22 having an F-number of 2.8. The optics are to beproduced using spherical or non-logarithmic aspherical surfaces. Thespecification also includes a depth of field (DOF), for objects in ascene 100, from approximately 10 cm to infinity. The DOF is the range ofobject distances from camera 20 for which the image generated by thecamera has an extent of an equivalent PSF, i.e., a PSF of an imageproduced by ISP 28 (FIG. 1), that is less than or equal to approximately5 μm. A more complete specification provided to step 50 is given inTable II below.

TABLE II Parameter Value Depth of Field 10 cm-infinity F-number 2.8Field of View 58°-62° Lens Total Track <6.4 mm Approximate Focal Length4.3 mm Back Focal Length >1.5 mm (includes an IR filter between thefinal lens and the sensor) Sensor: ⅓″ 2M CMOS Active Imager Size 4.48 mm(H) 3.36 mm (V), 5.60 mm diagonal Active Pixels 1600 (H) 1200 (V) PixelSize 2.8 μm (H) 2.8 μm (V)

In prior art systems, the depth of field of a camera is related to theF-number of the camera lens so that, for example, an F/2.8 lens has alargest depth of field when focused at the hyperfocal distance of thelens. In this case a depth of field of a 4.3 mm focal length lens isfrom infinity to of the order of 50 cm from the camera.

In addition to the specification generated in step 50, Zernikepolynomial coefficient values shown in Table III are provided forcontinuing to optical design step 52. The description hereinbelowassumes that the coefficient values are for Zernike fringe coefficients,Those skilled in the art will be able to convert the values for thefringe coefficients to Zernike standard coefficients, without undueexperimentation.

TABLE III Zernike Polynomial Fringe Coefficient Z4 0.9 Z9 0 Z16 −0.2 Z25−0.5 Z36 0 Z37 0.2

FIG. 9 shows detail of sensor 24, in accordance with an embodiment ofthe present invention. Sensor 24 comprises an array of 1200×1600 pixels,which deconvolution engine 26 processes as 192 sub-arrays of 100×100pixels. Because of the non-uniform performance of optics 22 over sensor24, as described above, deconvolution engine 26 applies a different15×15 pixel DCF kernel (FIGS. 5A, 5B, 5C) to each sub-array. However,since optics 22 are cylindrically symmetric, the same DCF kernel may beapplied to groups of four or eight sub-arrays of sensor 24. For example,the four sub-arrays 120 are all symmetric with respect to the center ofsensor 24, and so engine 26 may apply the same DCF kernel to the four.Similarly, the eight sub-arrays 122 are also symmetric with respect tothe center, so that engine 26 may apply the same DCF kernel to theeight. Inspection of the sub-arrays of sensor 24 shows that 33 differentDCF kernels suffice for engine 26 to process the complete sensor. EachDCF kernel applies to a group of sub-arrays, and each sub-array in agiven group subtends the same angle to the optic axis of the camera.

The DCF kernels are iteratively created in step 62, typically usingiterations of the optical design as described herein.

In an alternative embodiment of the present invention, sensor 24 isconsidered as 768 sub-arrays of 50×50 pixels. In the alternativeembodiment, deconvolution engine applies 768 respective DCF kernels tothe sub-arrays. An example of a DCF kernel for the alternativeembodiment, for a corner 50×50 array, is given in the matrix below.

$\quad\begin{Bmatrix}2 & 8 & 1 & {- 1} & 2 & 14 & 1 & 10 & 1 & 19 & 2 & 11 & 0 & 6 & 0 \\0 & {- 2} & 10 & 0 & {- 13} & 1 & 23 & 0 & 23 & {- 1} & 10 & 0 & 0 & {- 1} & {- 5} \\3 & 21 & {- 2} & {- 21} & {- 3} & {- 25} & {- 1} & {- 4} & 1 & {- 3} & 0 & {- 11} & {- 1} & 2 & 1 \\0 & 2 & 31 & {- 5} & {- 23} & {- 13} & {- 151} & {- 11} & {- 165} & {- 4} & {- 49} & 0 & 33 & 0 & {- 6} \\3 & 7 & 0 & {- 15} & {- 8} & 33 & {- 34} & {- 182} & {- 29} & {- 163} & {- 3} & {- 76} & 1 & 13 & 2 \\0 & {- 4} & {- 41} & {- 5} & {- 6} & 25 & 161 & {- 38} & 330 & {- 17} & {- 125} & 3 & 31 & {- 1} & 9 \\3 & 14 & {- 7} & {- 16} & {- 8} & {- 123} & 93 & 401 & 70 & 470 & {- 12} & {- 18} & 2 & {- 8} & 3 \\0 & 0 & 14 & {- 15} & {- 199} & {- 52} & 304 & 358 & 479 & {- 37} & {- 176} & {- 1} & {- 7} & {- 1} & 15 \\1 & 26 & 0 & 14 & {- 25} & {- 171} & 62 & 136 & {- 42} & 177 & {- 22} & {- 144} & 1 & {- 9} & 3 \\0 & {- 1} & 33 & {- 1} & {- 90} & {- 26} & {- 35} & {- 19} & {- 81} & {- 29} & {- 129} & {- 3} & {- 3} & {- 2} & 17 \\0 & 12 & 0 & 3 & {- 8} & {- 55} & {- 9} & 4 & {- 20} & {- 45} & {- 3} & {- 58} & {- 5} & 18 & 4 \\0 & {- 1} & 0 & 0 & 1 & 1 & {- 7} & 0 & 9 & 1 & {- 11} & {- 3} & {- 13} & {- 4} & 13 \\0 & 7 & {- 1} & {- 1} & 0 & 3 & 1 & {- 8} & 1 & {- 8} & 1 & 7 & {- 5} & {- 15} & 3 \\0 & {- 1} & {- 2} & 0 & 6 & 0 & 9 & 1 & 13 & 1 & 8 & {- 1} & 1 & {- 1} & 10 \\0 & 0 & 1 & 0 & 2 & 0 & 3 & 0 & 3 & 0 & 2 & 0 & 1 & 0 & 3\end{Bmatrix}$

The matrix above corresponds to a sub-array which subtends 33 degrees tothe optic axis of the camera. Those having ordinary skill in the artwill be able to produce DCF kernels for sub-arrays subtending otherangles to the optic axis, by the iterative methods described herein. Inone embodiment, application of the matrix above over other sub-arrays ofsensor 24 yielded satisfactory results.

In one embodiment of the present invention, the initial optical designuses a virtual or dummy phase element, as described above with referenceto step 52, and as exemplified below with reference to the flowchart ofFIG. 10. The virtual phase element is formed to have Zernikecoefficients with the same absolute value as those of Table III, butwith opposite sign.

FIG. 10 is a flowchart describing procedures performed in steps 52 and53 (FIG. 4), and FIGS. 11A, 11B, . . . , 11E, show results generated inthe procedures, in accordance with an embodiment of the presentinvention. In a modeling procedure 132, to evaluate the feasibility ofthe optical design, the optical designer may initially generate resultsfor an ideal lens with a focal length corresponding the specification ofTable II, together with a phase element having opposite Zernikecoefficients to those of Table III. In the following description, it isassumed that the specification is as given below for Table IV, withZernike coefficients as given below in Table V.

TABLE IV Parameter Value Depth of Field 10 cm-infinity F-number 2.8Field of View Approximately 66° Lens Total Track <4.6 mm ApproximateFocal Length 3.3 mm Back Focal Length >1.2 mm Sensor: ⅓″ 2M CMOS ActiveImager Size 4.48 mm (H) 3.36 mm (V), 5.60 mm diagonal Active Pixels 1600(H) 1200 (V) Pixel Size 2.8 μm (H) 2.8 μm (V)

TABLE V Zernike Polynomial Fringe Coefficient Z4 0.3 Z9 −0.4 Z16 0.1 Z250.0 Z36 0.0 Z37 0.0

An example of results generated in procedure 132 is given in FIG. 11A.

FIG. 11A shows graphs of optical path differences (OPDs) for an ideallens of focal length 3.3 mm combined with a phase element, in accordancewith an embodiment of the present invention. The OPD graphs plot thenumber of wavefronts (W) vs. PX, PY (μm) at wavelengths 486 nm and 656nm. Inspection of the graphs shows that they are relatively smooth, sothat it is likely that a final optical design corresponding to thespecifications of Tables IV and V will be successful. In the event thatthe graphs are not smooth, the final design may not be successful, sothat a change in the specifications may be advisable.

Returning to FIG. 10, in a classical design procedure 134, the opticaldesigner generates a best version of the lens assembly according to theinitial specifications, but ignoring the aberration specifications. Itwill be understood that for any given set of specifications, there aremany possible assemblies that may be considered, and that there are alsomany practical constraints. For example, the number of lenses may bevaried, although typically the fewer the lenses the lower the cost.Alternatively or additionally, the parameters associated with the lensmanufacture, such as a maximum angle made by a surface of the lensrelative to the optic axis, may be varied, although typically this maynot be more than 55°. From these assemblies and with regard to theconstraints, the designer selects a best version, and simulates resultsproduced by the version. The results typically include MTF curves, spotdiagrams, and Zernike polynomial coefficients. The MTF values aretypically high, corresponding to the overall good image qualitygenerated for a best version, whereas the spot diagrams and/orcoefficient distributions may be poor. Typical MTF results of theclassical design procedure are shown in FIG. 11B.

In a modified classical procedure 136, the designer attempts to improvethe spot diagrams and/or coefficient distributions, typically at thecost of reducing the MTF values. The improvement is usually achieved byapplying merit functions to the Zernike coefficients, to attempt toreduce the coefficients to zero over the complete field of view of theassembly. The application of merit functions is described above.Comparison of the results shown in FIG. 11C with those of FIG. 11B showsthat zeroing the Zernike coefficients in procedure 136 reduces the MTFvalues.

In a Zernike design procedure 138, a phase element with Zernikecoefficients having the same values as those of Table V is applied tothe version produced in procedure 136. Typically, a number of designsare produced incorporating the phase element, and each of the designs isadjusted to attempt to zero the final Zernike coefficients. Zeroing thefinal Zernike coefficients normally reduces the MTF of the design. Abest design is chosen from the designs found in this stage. FIG. 11Dshows examples of different MTF curves that may be produced by procedure138.

In a refinement procedure 140, the phase element is removed from thebest design chosen in procedure 138. The resulting design gives resultsshown in FIG. 11E and, as expected, the Zernike coefficient values areclose to those of the initial request. The resulting design may befurther refined to attempt to bring the coefficients closer to theinitial request. FIG. 11E shows examples of MTF curves and values ofZernike coefficients before and after the refinement procedure. In boththe design and the refinement procedures, in addition to bringing theZernike coefficients close to the initial request, the design isadjusted so that the MTF curves are all approximately the same shape.The conditions on the MTF curves, that the design meets, are describedin more detail with respect to FIGS. 12A-12G below.

The inventors have found that application of the procedures given inFIG. 10, together with the steps described in FIG. 4, gives a camerahaving a depth of field from approximately 10 cm to infinity. Theresulting value of Z4 is typically between approximately 0.6 andapproximately 0.9, but the inventors have found that Z4>approximately0.1 gives good results, and that deconvolution engine 26 may beconfigured to satisfactorily correct the aberrations producedcorresponding to these values of Z4, and to other non-zero values of theZernike coefficients. In addition, typically the coefficients of Z9, thethird order spherical aberration, are between approximately 0 andapproximately −0.2, the coefficients of Z16, the fifth order sphericalaberration, are between approximately −0.1 and approximately −0.3, thecoefficients of Z25, the seventh order spherical aberration, are betweenapproximately −0.4 and approximately −0.6, and the coefficients of Z36,the ninth order spherical aberration, are between approximately 0 andapproximately 0.2. The aberrations give an extent of the PSF that istypically greater than or equal to approximately 5 pixels, i.e., 14 μm,on sensor 24.

FIGS. 12A-12G shows MTF curves for an exemplary optical imaging assembly152, in accordance with an embodiment of the present invention.Exemplary assembly 152 is described in more detail with reference toFIG. 13 below, and is one example of assembly 22. Assembly 152 isdesigned according to the steps and procedures of FIGS. 4 and 10. TheMTF curves may be produced during, and/or at the conclusion of, thedesign.

FIG. 12A is for an object 100 mm from camera 20; FIG. 12B is for anobject 150 mm from the camera; FIG. 12C is for an object 200 mm from thecamera; FIG. 12D is for an object 300 mm from the camera; FIG. 12E isfor an object 500 mm from the camera; FIG. 12F is for an object 1000 mmfrom the camera; and FIG. 12G is for an object at infinity.

Each figure comprises four fields of view 0°, 12°, 25°, and 33°. Thesagittal (S) and tangential (T) orientation curves are shown for eachfield of view.

Inspection of the MTF curves shows that all MTF values for spatialfrequencies above approximately 50 cycles per mm are low, equalingapproximately 0.35 or less. The low MTF values are a consequence of thedistorted image on sensor 24. However, because the MTF values are allapproximately equal, the corrections applied by engine 26 generatesubstantially the same improvement to all the images, so as to produceapproximately equal and high MTFs for all the corrected images.

It will be understood that the above MTF properties are not just forassembly 152, but apply to a range of assemblies 22 generated accordingto the steps and procedures of FIGS. 4 and 10, generating a camera witha depth of field from approximately 10 cm to infinity.

FIG. 13 is a schematic diagram of optical imaging assembly 152, inaccordance with an embodiment of the present invention. Assembly 152comprises five components: an aperture 151, three lenses 154, 156, 158and an infra-red filter 160. Assembly 152 forms its image on a frontsurface 162 of sensor 24, so that the front surface acts as a focalplane of the assembly. Each lens has two aspheric surfaces, each surfacebeing defined by expression (6):

$\begin{matrix}{z = {\frac{c\; r^{2}}{1 + \sqrt{1 - {\left( {1 + k} \right)c^{2}r^{2}}}} + {\sum\limits_{n = 2}^{n = 8}{\alpha_{n}r^{2n}}}}} & (6)\end{matrix}$

where z is a surface sag,

-   -   r is a radius measured to an optic axis,    -   c, k are curvature and conic constants for the surface, and    -   α₂, . . . α₈ are parameters for the surface.

Tables VI, VII, and VIII below show dimensions in mm and parameters ofeach of the ten surfaces of the assembly. In the tables, the surfaces ofeach component are distinguished by a suffix A or B. Thus, aperture 151has surfaces 151A and 151B. In Table VI, the thickness gives thedistance, measured along the optic axis, to the next surface, and thusgives spacings between the components. Thus, aperture 151 has athickness of 5.0·10⁻² mm, the distance from surface 151B to thefollowing surface, 154A, is 1.1·10 ⁻², and the distance from the finalsurface of the assembly, surface 160B of filter 160, to the sensor, is8.61·10⁻¹ mm.

TABLE VI Curvature Semi- Conic Element and Surface Material (c)Thickness diameter constant (k) Aperture 151 A — — 5.00E−02 7.50E−01 — B1.10E−02 7.50E−01 — Lens 154 A E48R 9.57E−02 7.75E−01 8.50E−01 9.74E+01B −4.46E−01  8.17E−01 1.05E+00 0.00E+00 Lens 156 A OKP4 −7.60E−01 8.44E−01 1.24E+00 −3.37E+00  B −2.42E−01  6.31E−01 1.51E+00 2.38E+00Lens 158 A E48R 8.10E−01 1.00E+00 2.24E+00 −4.03E+00  B 5.17E−011.17E+00 2.35E+00 −4.07E+00  Filter 160 A BK7 0.00E+00 3.00E−01 2.55E+000.00E+00 B 0.00E+00 8.61E−01 2.55E+00 0.00E+00

TABLE VII Aspheric Parameter Surface ^(α)2 ^(α)3 ^(α)4 ^(α)5 154A−1.38E−02 −9.00E−01   2.83E+00 −2.26E+00  154B −9.83E−02 1.24E−01−4.25E−01 7.62E−01 156A −2.63E−01 3.81E−01 −4.78E−01 6.04E−01 156B−2.42E−01 3.23E−01 −2.94E−01 1.93E−01 158A −1.48E−02 1.01E−03  1.48E−03−5.69E−04  158B −2.29E−02 5.83E−03 −6.90E−04 −9.33E−05 

TABLE VIII Aspheric Parameter Surface ^(α)6 ^(α)7 ^(α)8 154A −2.96E+002.69E+00  1.61E+00 154B −8.04E−01 4.73E−01 −1.28E−01 156A −4.52E−011.58E−01 −1.74E−02 156B −7.36E−02 1.39E−02 −9.05E−04 158A  6.66E−052.82E−06 −9.13E−07 158B  3.50E−05 −2.76E−06  −3.27E−08

Plastic E48R is produced by Zeon Corporation of Tokyo, Japan and has arefractive index approximately equal to 1.53. Material OKP4 is producedby Osaka Gas Chemicals Ltd., of Japan and has a refractive indexapproximately equal to 1.61. Glass BK7 is produced by Schott AG ofMainz, Germany and has a refractive index approximately equal to 1.52.

Table IX below gives Zernike fringe coefficient values for assembly 152.

TABLE IX Zernike Fringe Coefficient Values. Angle subtended to opticaxis. 0.0° 12.08° 24.86° 32.98° Z1 1.00288770 1.02127383 0.962015000.85454775 Z2 0.00000000 0.00000000 0.00000000 0.00000000 Z3 0.00000000−0.05223421 0.05807529 −0.30413404 Z4 0.87386304 0.90256837 0.791785220.64302633 Z5 0.00000000 0.26444145 0.26333002 0.39499181 Z6 0.000000000.00000000 0.00000000 0.00000000 Z7 0.00000000 0.00000000 0.000000000.00000000 Z8 0.00000000 −0.11110116 −0.10841115 −0.29131996 Z90.01038369 0.02086120 −0.03451554 −0.13998095 Z10 0.00000000 0.000000000.00000000 0.00000000 Z11 0.00000000 −0.02198021 0.04819563 0.12033762Z12 0.00000000 −0.02888193 −0.03276898 −0.00332529 Z13 0.000000000.00000000 0.00000000 0.00000000 Z14 0.00000000 0.00000000 0.000000000.00000000 Z15 0.00000000 −0.08992847 −0.28884894 −0.49929953 Z16−0.17964427 −0.17714956 −0.20757048 −0.28003848 Z17 −0.00011960−0.01441891 −0.00335795 −0.04129877 Z18 0.00000000 0.00000000 0.000000000.00000000 Z19 0.00000000 0.00000000 0.00000000 0.00000000 Z200.00000000 −0.01596180 0.01304892 0.02364346 Z21 0.00000000 −0.03213805−0.01154570 0.05277862 Z22 0.00000000 0.00000000 0.00000000 0.00000000Z23 0.00000000 0.00000000 0.00000000 0.00000000 Z24 0.00000000−0.08180872 −0.20527244 −0.44185571 Z25 −0.48135930 −0.46936616−0.47693323 −0.52697618 Z26 0.00000000 0.00000000 0.00000000 0.00000000Z27 0.00000000 0.01252334 −0.01680502 −0.06101027 Z28 −0.000087010.00361287 0.00625800 −0.05449299 Z29 0.00000000 0.00000000 0.000000000.00000000 Z30 0.00000000 0.00000000 0.00000000 0.00000000 Z310.00000000 0.00651342 0.00031433 0.02571492 Z32 0.00000000 −0.00278981−0.02750737 −0.04436984 Z33 0.00000000 0.00000000 0.00000000 0.00000000Z34 0.00000000 0.00000000 0.00000000 0.00000000 Z35 0.000000000.05963151 0.13690960 0.06819783 Z36 0.00488173 0.00883963 0.01251918−0.07682018 Z37 0.19407879 0.18190738 0.14804313 0.08214757

Inspection of Table IX shows that for all fields of view the values ofZ4 are between approximately 0.6 and approximately 0.9, and the valuesof Z16 are between approximately −0.2 and approximately −0.3.Furthermore, the values of Z1, Z4, Z9, Z16, Z25, Z36, and Z37 in TableIX are all close to the target values in Table III.

Although the embodiments described above refer to certain specificdigital filters, and particularly to a deconvolution filter (DCF), theprinciples of the present invention may similarly be applied inelectronic cameras that use other types of digital image filters, as areknown in the art.

It will thus be appreciated that the embodiments described above arecited by way of example, and that the present invention is not limitedto what has been particularly shown and described hereinabove. Rather,the scope of the present invention includes both combinations andsubcombinations of the various features described hereinabove, as wellas variations and modifications thereof which would occur to personsskilled in the art upon reading the foregoing description and which arenot disclosed in the prior art.

1. An optical imaging assembly having cylindrical symmetry, comprising aplurality of lenses having surfaces with curvatures and spacings betweenthe surfaces, such that an optical image formed by the plurality oflenses has a defocus aberration coefficient greater than 0.1 at a focalplane of the assembly.
 2. The assembly according to claim 1, wherein thedefocus aberration coefficient is greater than or equal to 0.6.
 3. Theassembly according to claim 2, wherein the defocus aberrationcoefficient is less than or equal to 0.9.
 4. The assembly according toclaim 3, wherein a fifth order spherical aberration is between −0.2 and−0.3.
 5. The assembly according to claim 4, wherein a seventh orderspherical aberration is −0.5.
 6. The assembly according to claim 5,wherein a ninth order spherical aberration is
 0. 7. The assemblyaccording to claim 1, wherein the curvatures are non-logarithmic.
 8. Theassembly according to claim 1, wherein the optical image is of one ormore objects within a field of view subtending up to 330 to an opticaxis of the assembly.
 9. The assembly according to claim 1, wherein theoptical image is of one or more objects which are located at distancesgreater than or equal to 10 cm from the assembly.
 10. The assemblyaccording to claim 9, wherein the assembly is configured so that amodulation transfer function generated by the one or more objects at thefocal plane is less than or equal to 0.35 for spatial frequenciesgreater than 50 cycles per mm.
 11. The assembly according to claim 1,wherein the optical image has an extent of a point spread function equalto or greater than 14 μm at the focal plane.
 12. A method for opticalimaging, comprising: formulating an optical specification of an opticalimaging assembly comprising optical elements having surfaces, theoptical specification comprising one or more aberration coefficients;generating a virtual phase element having phase coefficients which arenegatives of the aberration coefficients; generating a design of theoptical assembly comprising the optical elements and the virtual phaseelement so as to determine curvatures and spacings of the surfaces thatwill focus an image of an object on a focal plane of the assembly in thepresence of the virtual phase element; and fabricating the opticalassembly in accordance with the curvatures and spacings determined bythe design.
 13. The method according to claim 12, wherein the aberrationcoefficients comprise a defocus aberration coefficient greater than 0.1.14. The method according to claim 13, wherein the defocus aberrationcoefficient is greater than or equal to 0.6.
 15. The method according toclaim 14, wherein the defocus aberration coefficient is less than orequal to 0.9.
 16. The method according to claim 15, wherein the one ormore aberrations comprise a fifth order spherical aberration that isbetween −0.1 and −0.3.
 17. The method according to claim 12, wherein thecurvatures are non-logarithmic.
 18. The method according to claim 12,wherein the optical specification comprises a field of view of theobject subtending up to 33° to an optic axis of the assembly.
 19. Themethod according to claim 12, wherein the optical specificationcomprises a distance of the object from the assembly being greater thanor equal to 10 cm from the assembly.
 20. The method according to claim19, wherein the optical specification comprises a modulation transferfunction generated by the object at the focal plane being less than orequal to 0.35 for spatial frequencies greater than 50 cycles per mm. 21.The method according to claim 12, wherein the image has an extent of apoint spread function equal to or greater than 14 μm at the focal plane.22. The method according to claim 12, and comprising generating adigital filter to compensate for the one or more aberrationcoefficients, and coupling the digital filter to the optical assembly sothat a filtered image formed by the digital filter from the image on thefocal plane is free of aberrations.
 23. The method according to claim22, wherein the filtered image is free of aberrations for the objectbeing located at a distance greater than 10 cm from the opticalassembly.
 24. An optical imaging assembly having cylindrical symmetry,comprising a plurality of lenses having surfaces with curvatures andspacings between the surfaces, such that an optical image formed by theplurality of lenses at a focal plane of the assembly has a modulationtransfer function (MTF) for spatial frequencies greater than 50 cyclesper millimeter that is less than or equal to 0.35.
 25. A method forforming an optical imaging assembly, comprising: providing a pluralityof lenses having cylindrical symmetry and surfaces with curvatures andspacings between the surfaces; and arranging the lenses so that anoptical image formed by the plurality of lenses has a defocus aberrationcoefficient greater than 0.1 at a focal plane of the assembly. 26.Apparatus for optical imaging, comprising: an optical imaging assemblycomprising optical elements having surfaces; and a processor which isconfigured to: formulate an optical specification of the optical imagingassembly, the optical specification comprising one or more aberrationcoefficients, generate a virtual phase element having phase coefficientswhich are negatives of the aberration coefficients; generate a design ofthe optical assembly comprising the optical elements and the virtualphase element so as to determine curvatures and spacings of the surfacesthat will focus an image of an object on a focal plane of the assemblyin the presence of the virtual phase element; and fabricate the opticalassembly in accordance with the curvatures and spacings determined bythe design.
 27. A method for forming an optical imaging assembly,comprising: providing a plurality of lenses having cylindrical symmetryand surfaces with curvatures and spacings between the surfaces; andarranging the lenses so that an optical image formed by the plurality oflenses at a focal plane of the assembly has a modulation transferfunction (MTF) for spatial frequencies greater than 50 cycles permillimeter that is less than or equal to 0.35.
 28. An optical imagingassembly, comprising: an aperture having a semi-diameter of 7.5·10⁻¹ mm;and a plurality of lenses having surfaces with curvatures and spacingsbetween the surfaces, wherein respective surfaces of the plurality oflenses are defined by an equation$z = {\frac{c\; r^{2}}{1 + \sqrt{1 - {\left( {1 + k} \right)c^{2}r^{2}}}} + {\sum\limits_{n = 2}^{n = 8}{\alpha_{n}r^{2n}}}}$where z is a sag of the surface, r is a radius measured to an optic axisof the assembly, c, k are respective curvature and conic constants forthe surface, and α₂, . . . α₈ are parameters for the surface, the lensescomprising: a first aspheric lens following the aperture, having arefractive index 1.53, a first surface wherein c=9.57·10⁻², k=9.74·10¹,α₂=−1.38·10⁻², α₃=−9.0·10⁻¹, α₄=2.83, α₅=−2.26, α₆=−2.96, α₇=2.69,α₈=1.61, and a second surface wherein c=−4.46·10⁻¹, k=0, α₂=−9.83·10⁻²,α₃=1.24·10⁻¹, α₄=−4.25·10⁻¹, α₅=7.62·10⁻¹, α₆=−8.04·10⁻¹, α₇=4.73·10⁻¹,α₈=−1.28·10⁻¹; a second aspheric lens following the first aspheric lens,having a refractive index 1.61, a third surface wherein c=−7.60·10⁻¹,k=−3.37, and absolute values of α₂, α₃, α₄, α₅, α₆, α₇, α₈ less than 1,and a fourth surface wherein c=−2.42·10⁻¹, k=2.38, and absolute valuesof α₂, α₃, α₄, α₅, α₆, α₇, α₈ less than 1; and a third aspheric lensfollowing the second aspheric lens, having a refractive index 1.53, afifth surface wherein c=8.1·10⁻¹, k=−4.03, and absolute values of α₂,α₃, α₄, α₅, α₆, α₇, α₈ less than 1, and a sixth surface whereinc=5.17·10⁻¹, k=−4.07, and absolute values of α₂, α₃, α₄, α₅, α₆, α₇, α₈less than 1.